2007 Pulsed Power and Plasma Science Conference Albuquerque, NM 6E5 Dispersion relation of dust acoustic waves in a DC glow discharge plasma Bob Merlino, Ross Fisher, Univ. Iowa Ed Thomas, Jr. Auburn Univ. Work supported by NSF and DOE Dust acoustic waves (Rao, Shukla, Yu, Planet. Space. Sci. 38, 543, 1990) • very low frequency (<< wp+, phase speed Csd << v+,th) longitudinal compressional disturbances in a fluid-like dusty plasma • the dust particles participate in the wave dynamics – it is a “dust wave” • phase speed (dust acoustic speed) CDA kT ~ Z md 2 Dust acoustic waves: fluid theory Dust dynamics Electrons & Ions Quasineutrality K Dd 1 nd (nd vd ) 0 t x vd nd vd md nd vd kTd eZ d nd 0 x x x t ne n kTe ene 0; kT en 0 x x x x (e o )(n ne Znd ) 2 n ne Z d nd Combining the dust momentum equation with the plasma equations we see that (for the case of cold dust, Td = 0). vd md nd ( Pe P ) t x where Pe + P+ is the total pressure due to electrons and ions. In the dust acoustic wave the inertia is provided by the massive dust particles and the electrons and ions provide the restoring force excitation of dust acoustic waves • dust acoustic waves can be driven by an ion-dust streaming instability (Rosenberg, JVST A 14, 631, 1996) • a relatively modest drift uo~ vith of the ions through the dust is sufficient for instability • DAWs are spontaneously excited in dusty plasmas produced in gas discharges • are observed visually by laser light scattering dust acoustic dispersion relationship (Td ~ 0) acoustic modes (long wavelength) 2 w kT Z K md T 1 1 Z Te n w here: d ni Finite KD effects: w K w here: 2D 1 2De 2 w CDA K Effect of dust-gas collisions: 2 w w ib K 2CDA 1 2 C DA 2 2 2 1 K D 1 1 b is the dust-neutral collision frequency 1 2Di Dust acoustic waves cm Measurement of the dispersion relationship of the dust acoustic wave Original Experiments A. Barkan, N. D’Angelo, and R. L. Merlino, Phys. Plasmas, 2, 3563 (1995). C. Thompson, A. Barkan, N. D’Angelo, and R. L. Merlino, Phys. Plasmas, 4, 2331 (1997). New measurements of dust acoustic waves • Over the past decade, numerous experimental and theoretical studies of DAW’s have been made. • These studies have all been in the “linear” regime of the DAW dispersion. • Goal of new studies: extend dispersion relation measurements to finite kD regime. UI dusty plasma device Ar, 50 -150 mtorr LASER ANODE GLOW B ANODE DUST 300 – 400 V ~ 1 mA Parameters plasma density ~ 108 – 109 cm-3 Te ~ 2 – 3 eV, T+ ~ 0.025 eV Dust: kaolin powder -average dust radius ~ 1 micron average dust charge Z ~ – (1000 – 2000) dust density nd ~ 105 cm-3, wpd ~ 300 - 500 s-1 For current modulation 60 cm dia. x 80 cm long vacuum vessel dc glow discharge plasmas (N2, Ar) 50 - 100 G axial magnetic fields Experiment at Univ. of Iowa, Fall, 2006 Dust acoustic waves are captured using a 30 fps digital camera single frame video images of DAW Natural 65 kHz 39 kHz 130 kHz video analysis About 100 images were analyzed for each frequency w (s–1) dispersion relation (long wavelength) K (cm–1) dispersion relation short wavelengths Td = 40 eV w (s ) ) w (s–1–1 Td = 10 eV K (cm–1) Hot dust? • J. Williams and E. Thomas, Jr. (IEEE TPS 35, 303, 2007) measured dust temperatures for dust embedded in a dc glow discharge • Method- stereoscopic particle image velocimetry, determined Td in 3 directions • Found Td’s ~ tens of eV at comparable pressures as those used here Weakly vs. strongly coupled? 1000 2 d Q 4 o kTd 100 10 1 0.1 0.01 0.1 1 10 Dust temperature, eV If dust were cold, would be large and dust would be in strongly coupled state, which it isn’t. 100 summary • DAWs were investigated in a dc glow discharge plasma • DAWs appear spontaneously, but their frequency can be controlled by modulating the discharge current • Frequencies up to ~ 200 Hz were studied to measure the DAW dispersion relation • interference of spontaneously excited DAW and high frequency, imposed DAW was observed • Comparison with theory requires that the dust is hot, with Td ~ 10s of eV.